Interference of Waves

As most commonly used, the term interference usually refers to the interaction of waves which are correlated or coherent with each other, either because they come from the same source or because they have the same or nearly the same frequency.
Wave interference is the phenomenon which occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape which results from the net effect of the two individual waves upon the particles of the medium.

Consider two waves that are in phase,with amplitudes A1 and A2. Their troughs and peaks line up and the resultant wave will have amplitude A = A1 + A2. This is known as constructive interference — a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the same direction.

If the two waves are pi radians, or 180°, out of phase, then one wave’s crests will coincide with another wave’s troughs and so will tend to cancel out. The resultant amplitude is A = | A1A2 | . If A1 = A2, the resultant amplitude will be zero. This is known as destructive interference — a type of interference which occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction.


When two sinusoidal waves superimpose, the resulting waveform depends on the frequency (or wavelength) amplitude and relative phase of the two waves. If the two waves have the same amplitude A and wavelength the resultant waveform will have an amplitude between 0 and 2A depending on whether the two waves are in phase or out of phase.
The task of determining the shape of the resultant demands that the principle of superposition is applied. The principle of superposition is sometimes stated as follows: When two waves interfere, the resulting displacement of the medium at any location is the algebraic sum of the displacements of the individual waves at that same location.

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